Estimation of Population Parameters

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Estimation of Population Parameters

Aim

Undertake a small-scale survey to estimate population parameters.

Size of Sample

The size of the sample must be quite small, because it is stated so in

the aim. However, to make accurate estimates of population parameters

the sample must be large enough.

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According to the Central Limit Theorem:

n If the sample size is large enough, the distribution of the sample

mean is approximately Normal.

n The variance of the distribution of the sample mean is equal to the

variance of the sample mean divided by the sample size.

These are true whatever the distribution of the parent population. The

Central Limit Theorem allows predictions to be made about the

distribution of the sample mean without any knowledge of the

distribution of the parent population, as long as the sample is large

enough.

For this reason, the sample size will be set at 50, which I consider

large enough for the distribution of its mean to be normal (according

to the Central Limit Theorem). It should not be larger because the aim

of this investigation is to carry out a “small scale survey”

How / What Data to be Collected

The sample will be of the weight of 50 smarties. To be a “good”

sample, that is that the results are valid and not biased in any way,

these smarties must be collected randomly. 10 tubes of smarties will

be bought, each from a different shop, and 5 will be selected at

random from each tube to be used in the survey. This should produce a

random sample.

The sample must be random for the Central Limit Theorem to be in

effect, so that the distribution of its mean is Normal and predictions

can be made about it, even though the distribution of the parent

population of smarties is unknown and not necessarily Normal.

What Calculations will be Made Using the Data

n The mean, standard deviation and variance of the sample.

n These will be used to estimate the variance and standard deviation

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